For what value of x are the points A(–3, 12), B(7, 6) and C(x, 9) collinear?

To show that the points are collinear, we show that the area of triangle is equilateral = 0


Δ = 0


Δ = 1/2{x1(y2−y3) + x2(y3−y1) + x3(y1−y2)}


Δ = 1/2{–3(6–9) + 7 (9 – 12) + x(12– 6)} = 0


(–3)(–3) + 7(–3) + 6x = 0


9–21 + 6x = 0


6x = 12


x = 2


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